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Mapping a shape to some parametric domain is a fundamental tool in graphics and scientific computing. In practice, a map between two shapes is commonly represented by two meshes with same connectivity and different embedding. The standard…
With the surge of multi- and manycores, much research has focused on algorithms for mapping and scheduling on these complex platforms. Large classes of these algorithms face scalability problems. This is why diverse methods are commonly…
We study the efficient generation of random graphs with a prescribed expected degree sequence, focusing on rank-1 inhomogeneous models in which vertices are assigned weights and edges are drawn independently with probabilities proportional…
Graph isomorphism problem is a known hard problem. In this paper, a novel randomized algorithm is proposed for this problem which is very simple and fast. It solves the graph isomorphism problem with running time O(n^2.373) for any pair of…
High-definition (HD) map is a fundamental component of autonomous driving systems, as it can provide precise environmental information about driving scenes. Recent work on vectorized map generation could produce merely 65% local map…
We use some fundamental ideas from complex analysis to create symmetric images and animations. Using a domain coloring algorithm, we generate mappings to the entire complex plane or the hyperbolic upper half-plane. The resulting designs can…
Maps are a very important component of strategy games, and a time-consuming task if done by hand. Maps generated by traditional PCG techniques such as Perlin noise or tile-based PCG techniques look unnatural and unappealing, thus not…
Two graphs $G$ and $H$ are \emph{cospectral} if the adjacency matrices share the same spectrum. Constructing cospectral non-isomorphic graphs has been studied extensively for many years and various constructions are known in the literature,…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
The Subgraph Isomorphism problem asks, given a host graph G on n vertices and a pattern graph P on k vertices, whether G contains a subgraph isomorphic to P. The restriction of this problem to planar graphs has often been considered. After…
A mobility map, which provides maximum achievable speed on a given terrain, is essential for path planning of autonomous ground vehicles in off-road settings. While physics-based simulations play a central role in creating next-generation,…
A GraphMaps is a system that visualizes a graph using zoom levels, which is similar to a geographic map visualization. GraphMaps reveals the structural properties of the graph and enables users to explore the graph in a natural way by using…
The synthesis of a metasurface exhibiting a specific set of desired scattering properties is a time-consuming and resource-demanding process, which conventionally relies on many cycles of full-wave simulations. It requires an experienced…
The perception of high-definition maps is an integral component of environmental perception in autonomous driving systems. Existing research have often focused on online construction of high-definition maps. For instance, the Maptr[9]…
Closed-form generating functions for counting one-face rooted hypermaps with a known number of darts by number of vertices and edges is found, using matrix integral expressions relating to the reduced density operator of a bipartite quantum…
In the past decades for more and more graph classes the Graph Isomorphism Problem was shown to be solvable in polynomial time. An interesting family of graph classes arises from intersection graphs of geometric objects. In this work we show…
In this paper, we introduce orbit matrices of directed strongly regular graphs (DSRGs). Further, we propose a method of constructing directed strongly regular graphs with prescribed automorphism group using genetic algorithm. In the…
Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the…
We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property…